Simplify to lowest terms. $\dfrac{36}{40}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 36 and 40? $36 = 2\cdot2\cdot3\cdot3$ $40 = 2\cdot2\cdot2\cdot5$ $\mbox{GCD}(36, 40) = 2\cdot2 = 4$ $\dfrac{36}{40} = \dfrac{9 \cdot 4}{ 10\cdot 4}$ $\hphantom{\dfrac{36}{40}} = \dfrac{9}{10} \cdot \dfrac{4}{4}$ $\hphantom{\dfrac{36}{40}} = \dfrac{9}{10} \cdot 1$ $\hphantom{\dfrac{36}{40}} = \dfrac{9}{10}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{36}{40}= \dfrac{2\cdot18}{2\cdot20}= \dfrac{2\cdot 2\cdot9}{2\cdot 2\cdot10}= \dfrac{9}{10}$